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This book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasizes the relation between microscopic reversibility and macroscopic irreversibility. Students will find a clear and detailed explanation of fundamental concepts such as equipartition, entropy, and ergodicity. They will learn about Brownian motion, the modern treatment of the thermodynamic limit phase transitions, the microscopic and macroscopic theory of the coexistence of phases, statistical mechanics of stationary states, and fluctuations and dissipation in chaotic motions.

Statistical physics --- Statistical mechanics. --- Mécanique statistique --- Mécanique statistique --- Statistical physics. --- Dynamical systems. --- Thermodynamics. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Mathematical statistics --- Statistical methods --- Quantum statistics --- Thermodynamics

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Statisticians of the Centuries aims to demonstrate the achievements of statistics to a broad audience, and to commemorate the work of celebrated statisticians. This is done through short biographies that put the statistical work in its historical and sociological context, emphasizing contributions to science and society in the broadest terms rather than narrow technical achievement. The discipline is treated from its earliest times and only individuals born prior to the 20th Century are included. The volume arose through the initiative of the International Statistical Institute (ISI), the principal representative association for international statistics (founded in 1885). Extensive consultations within the statistical community, and with prominent members of ISI in particular, led to the names of the 104 individuals who are included in the volume. The biographies were contributed by 73 authors from across the world. The editors are the well-known statisticians Chris Heyde and Eugene Seneta. Chris Heyde is Professor of Statistics at both Columbia University in New York and the Australian National University in Canberra. He is also Director of the Center for Applied Probability at Columbia. He has twice served as Vice President of the ISI, and also as President of the ISI's Bernoulli Society. Eugene Seneta is Professor of Mathematical Statistics at the University of Sydney and a Member of the ISI. His historical writings focus on 19th Century France and the Russian Empire. He has taught courses on the history of probability-based statistics in U.S. universities. Both editors are Fellows of the Australian Academy of Science and have, at various times, been awarded the Pitman Medal of the Statistical Society of Australia for their distinguished research contributions.

Mathematical statistics --- Mathematician. Statistician. Logici --- Statisticians --- AA / International- internationaal --- 300 --- 08 --- Algemene statistische naslagwerken. --- Biografieën en memoires. --- Statistics. --- Statistical physics. --- Dynamical systems. --- Statistics, general. --- Statistical Physics, Dynamical Systems and Complexity. --- Biography. --- Mathematicians --- Biografieën en memoires --- Algemene statistische naslagwerken --- Mathematics --- Mathématiques --- Mathématiciens --- History. --- Histoire. --- Statistics . --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Mathématiques --- Histoire --- Statisticians - Biography. --- Biographie --- Statistics - history --- Statistics - biography

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Synchronization: From Simple to Complex is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from human heart to neural networks. The authors study this phenomenon as applied to oscillations of different nature such as those with periodic, chaotic, noisy and noise-induced nature, reveal the general mechanisms behind synchronization, and bring to light other important effects that accompany synchronization such as phase multistability, dephasing and multimode interaction. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating system can be described in the framework of the general approach.

Nonlinear oscillations. --- Synchronization. --- Synchronization --- Nonlinear oscillations --- Sciences - General --- Physical Sciences & Mathematics --- Synchronism --- Physics. --- Statistical physics. --- Dynamical systems. --- Engineering. --- Statistical Physics, Dynamical Systems and Complexity. --- Theoretical, Mathematical and Computational Physics. --- Engineering, general. --- Nonlinear theories --- Oscillations --- Time measurements --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Construction --- Industrial arts --- Technology --- Statistical methods --- Mathematical physics. --- Physical mathematics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics

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Hydrodynamics --- Topology --- Hydrodynamique --- Topologie --- EPUB-LIV-FT SPRINGER-B --- Hydrodynamics. --- Mathematics. --- Fluids. --- Statistical physics. --- Dynamical systems. --- Computational intelligence. --- Mathematics, general. --- Fluid- and Aerodynamics. --- Statistical Physics, Dynamical Systems and Complexity. --- Computational Intelligence. --- Topology. --- Engineering. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Hydraulics --- Hydrostatics --- Permeability --- Math --- Science --- Statistical methods --- Fluid dynamics

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This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations.  Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations.      This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks. With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.

Evolution equations. --- Engineering. --- Applications of Graph Theory and Complex Networks. --- Graph Theory. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Complex Systems. --- Complexity. --- Construction --- Industrial arts --- Technology --- Physics. --- Graph theory. --- Statistical physics. --- System theory. --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Systems, Theory of --- Systems science --- Science --- Physics --- Mathematical statistics --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Philosophy --- Statistical methods --- Extremal problems